Perhaps I should quantify. My cage is 2ft in diameter - which is 1ft from bulbs to cage in any direction. The plant pots themselves are a little further away than this, but as they grow they lean into the cage. As you know, I use my cage to vertically scrog, so I just fill in the gaps as they grow, weaving branches in, out and up (and sometimes down).
If the grow gets a bit tight, it's usually because I have too many plants of the same strain crammed around the lights, or am growing indica or indica hybrid varieties that stay short and squat. While this is all part of dialing in each grow, I do tend to remove fan leaves if they get in the way - which is why I don't mind burning them, and the plants don't seem to mind losing them.
Fan leaves are mainly there to store and supply nutrients and photosynthesise energy for branch and root growth, which slows as the plant starts to flower. Removing fans leaves in the flowering stage allows more light to get to the bud sites and - as long as the plant gets enough food - allows those sites to photosynthesise more efficiently and bloom.
The trick to removing fan leaves is to take the ones at the base of the main branches (where they jut out of the main stem/s) and try to leave the ones that are on the branches nearer the bud sites. The fan leaves that jut out from the main stem have already served their main purpose: to provide food and energy for the branches and roots to grow - especially during the stretching phase of 12/12. After that, the smaller leaves, branches and bud sites take over.
Another trick is to arrange your plants SHORT, TALL, SHORT, TALL, around the lights so that the short plants fill in the gaps below, and the tall plants fan out and fill in the gaps above.
Finally, you can always move your pots back a little to give them more space and simply lean the bigger branches up against the cage, while the others support themselves. However, in my experience, overcrowding simply leads to smaller, fluffier buds, crappier yields and lots more trimming!
A vertical grow pretty much involves tweaking all the way. It's not for the hands-off grower: I always spend a bit of time weaving branches around to maximise their exposure to light. And yes, I have tried placing the plants further out from the light, but the yields tend to be poorer for the reason explained above.
My theory is this: if the tips of the fan leaves are burning, then the buds are in exactly the right position - not too close (to burn) and not too far away. I use the fan leaves as a measuring stick. Then I start to remove them once they've served their purpose. I've been doing it for years and it doesn't seem to affect yields. Hazes tend not to get in the way and obstruct everything like indicas, so I tend not to remove as many fan leaves from my sativa varieties. Hardly any, in fact.
I don't use cool tubes, either. As mentioned in another thread, they just get dirty and obstruct the light. You have to clean the outside AND inside of the tubes regularly (they can get pretty dirty in the two months during a grow), so it's not worth the hassle. There's no benefit, either, if you have good ventilation and a decent floor fan blowing up a cool column of air. This I have experimented with and is why I don't do it anymore.
I don't know what strain you're growing, but maybe you can experiment with growing 8 plants further away versus 6 plants in a little closer. I generally have about 6 plants around my 1200w grows. Sometimes 7 or 8 max, but that's usually if I have a staggered grow where some plants finish much earlier than others. The fast-finishing plants get removed after 7 weeks or so, and the haze hybrids are left to stretch out for another 2-3 weeks.